I've looked for songs that matched that simplicity. I like Enya's version, but Enya can't do simple; her songs get big without her even trying. Kelly Clarkson has a decent version, but Paula would never forgive me for picking a version with Reba on it.
Back we go to this year's shortstop of Christmas songs: Pentatonix. The five don't over-produce this song. It's clear that they don't do multiple tracks for anyone, and they give a very basic performance that I love.